### Decimal Fraction

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## Fraction

Fraction
1. Definition : A fraction is an expression that indicates the quotient of two quantities.

Ex :
2
1
,
3
1
,
5
6
, -
5
8
.

A fraction has two parts, Numerator and Denominator. Numerator is the number at the top of the fraction and denominator is the number at the bottom of the fraction.

2.Type of Fractions

i. Common Fraction : A common fraction (also known as Vulgar fraction and simple fraction) is a fraction in which both numerator and denominator are integers (As with other fractions, the denominator cannot be zero)

3
2
,
12
7
, -
3
2
,

ii. A decimal fraction is a fraction in which denominator is an integer power of ten. (The term decimals are commonly used to refer decimal fractions).

10
1
= 0.1

100
1
= 0.01

100
17
= 0.17

3. Annexing Zeros to the extreme right of a decimal fraction

Annexing zeros to the extreme right of a decimal fraction does not change its value.
Examples
0.4 = 0.40 = 0.400 = 0.4000, etc.
1.21 = 1.210 = 1.2100 = 1.21000, etc

4. Some Basic Formulae:
(a + b)(a - b) = (a2 - b2)
(a + b)2 = (a2 + b2 + 2ab)
(a - b)2 = (a2 + b2 - 2ab)
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
(a3 + b3) = (a + b)(a2 - ab + b2)
(a3 - b3) = (a - b)(a2 + ab + b2)
(a3 + b3 + c3 - 3abc) = (a + b + c)(a2 + b2 + c2 - ab - bc - ac)
When a + b + c = 0, then a3 + b3 + c3 = 3abc.